In common data analytic scenarios, data is produced by a multitude of _data producers_ (e.g., medical clinics), stored and maintained by some _data keeper_ (e.g., a centralized repository), and substantial benefit can be gained from making data accessible to a variety of _data consumers_ (e.g., researchers); however, making cleartext data accessible poses a privacy threat and may infringe on privacy regulation. Computing over data encrypted by fully homomorphic encryption (FHE) enables providing privacy guarantee together with data mining utility. To ensure that correct insights are extracted, it is essential to guarantee _data authenticity_. In this work we present an authenticity proof for encrypted data: As a central tool we show how to modify a classical MAC based on universal hashing to introduce _the first MAC with fast homomorphic verification over the reals_ (7.37 microseconds amortized runtime). We then utilize our MAC for guaranteeing data authenticity, for data provided by an untrusted data keeper in FHE encrypted form. We implemented our solution, demonstrating _substantial efficiency improvements_ over the prior art (Chatel et al. USENIX'21): improving the proof size and generation time by over 10^4X. To demonstrate the usefulness of our homomorphic verification in realistic systems we implemented it in AWS EC2 with S3 storage, demonstrating it achieves practical performance for fetching and authenticating FHE ciphertexts, as well as smooth integration with subsequent homomorphic evaluation of decision tree models.

This paper is an extended abstract of the recently published journal article (M. Goldenberg, The Heuristic Search Research Framework. Knowledge-Based Systems 129: 1–3. 2017). The Heuristic Search Research Framework is a software framework for implementing heuristic search algorithms and exploring their properties. The framework uses policy-based design to enable efficient, flexible and well-organized implementations. In addition, the framework provides effective tools for exploring the properties of the implemented algorithms. The extensive online documentation includes a video demo.

Multi-agent pathfinding (MAPF) is an area of expanding research interest. At the core of this research area, numerous diverse search-based techniques were developed in the past 6 years for optimally solving MAPF under the sum-of-costs objective function. In this paper we survey these techniques, while placing them into the wider context of the MAPF field of research. Finally, we provide analytical and experimental comparisons that show that no algorithm dominates all others in all circumstances. We conclude by listing important future research directions.

In this paper we study the k goal search problem (kGS), which is the problem of solving k shortest path problems that share the same start state. Two fundamental heuristic search approaches are analyzed: searching for the k goals one at a time, or searching for all k goals together in a single pass. Key theoretical properties are established and a preliminary experimental evaluation is performed.

When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f (n). n is re-inserted in the OPEN list with the f -cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain- and heuristic- specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

It is known that A* is optimal with respect to the expanded nodes (Dechter and Pearl 1985) (D&P). The exact meaning of this optimality varies depending on the class of algorithms and instances over which A* is claimed to be optimal. A* does not provide any optimality guarantees with respect to the generated nodes. However, such guarantees may be critical for optimally solving instances of domains with a large branching factor. In this paper, we introduce two new variants of the recently introduced Enhanced Partial Expansion A* algorithm (EPEA*) (Felner et al. 2012). We leverage the results of D&P to show that these variants possess optimality with respect to the generated nodes in much the same sense as A* possesses optimality with respect to the expanded nodes. The results in this paper are theoretical. A study of the practical performance of the new variants is beyond the scope of this paper.

A* is often described as being `optimal', in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. n is re-inserted into the OPEN list, but with the f-cost of the next best child. This paper introduces an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* generates only the children with the same f-cost as the parent. EPEA* is generalized to its iterative-deepening variant, EPE-IDA*. For some domains, these algorithms yield substantial performance improvements. State-of-the-art results were obtained for the pancake puzzle and for some multi-agent pathfinding instances. Drawbacks of EPEA* are also discussed.

A* is often described as being 'optimal,' in that it expands the minimum number of unique nodes. But, A* may generate many extra nodes which are never expanded. This is a performance loss, especially when the branching factor is large. Partial Expansion A* (PEA*) addresses this problem when expanding a node, n, by generating all the children of n but only storing children with the same f-cost as n. We introduce an enhanced version of PEA* (EPEA*). Given a priori domain knowledge, EPEA* only generates the children with the same f-cost as the parent. State-of-the-art results were obtained for a number of domains. Drawbacks of EPEA* are also discussed. A full version of this paper appears in the proceedings of AAAI-2012

Several variants of A* have been recently proposed for find-ing optimal solutions for the multi-agent pathfinding (MAPF)problem. We describe the application of the new enhancedpartial-expansion technique to MAPF, show how patterndatabases can be applied on top of this technique and com-pare the different A* variants experimentally.

The differential heuristic (DH) is an effective memory-based heuristic for explicit state spaces. In this paper we aim to improve its performance and memory usage. We introduce a compression method for DHs which stores only a portion of the original uncompressed DH, while preserving enough information to enable efficient search. Compressed DHs (CDH) are flexible and can be tuned to fit any size of memory, even smaller than the size of the state space. Furthermore, CDHs can be built without the need to create and store the entire uncompressed DH. Experimental results across different domains show that, for a given amount of memory, a CDH significantly outperforms an uncompressed DH.

We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional single-agent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search tree called the increasing cost tree (ICT) and a corresponding search algorithm that finds optimal solutions. We analyze this new formalization and compare it to the previous state-of-the-art A*-based approach. Experimental results on various domains show the benefits and drawbacks of this approach. A speedup of up to 3 orders of magnitude was obtained in a number of cases.

The differential heuristic (DH) is an effective memory-based heuristic for explicit state spaces. In this paper, we aim to improve its performance and memory usage. We introduce a compression method for DHs which stores only a portion of the original uncompressed DH, while preserving enough information to enable efficient search. Compressed DHs (CDH) can be tuned to fit any size of memory, even smaller than the size of the state space.Experimental results across different domains show that, for a given amount of memory, a CDH significantly outperforms an uncompress

We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional single-agent search variants of the A* algorithm. In Sharon et. al. (2011), we introduced a novel two-level search algorithm framework for this problem. The high-level searches a novel search tree called increasing cost tree (ICT). The low-level performs a goal test on each ICT node. The new framework, called ICT search (ICTS), showed to run faster than the previous state-of-the-art A* approach by up to three orders of magnitude in many cases. In this paper we focus on the low-level of ICTS which performs the goal test. We introduce a number of optional pruning techniques that can significantly speed up the goal test. We discuss these pruning techniques and provide supporting experimental results.

True distance memory-based heuristics (TDHs) were recently introduced as a way to obtain admissible heuristics for explicit state spaces. In this paper, we introduce a new TDH, the portal-based heuristic. The domain is partitioned into regions and portals between regions are identified. True distances between all pairs of portals are stored and used to obtain admissible heuristics throughout the search. We introduce an A*-based algorithm that takes advantage of the special properties of the new heuristic. We study the advantages and limitations of the new heuristic. Our experimental results show large performance improvements over previously-reported TDHs for commonly used classes of maps.